8. Consider the ellipse centered at (2,-1) with axes as shown in the figure below.
Its equation is:
A. 4x^{2}+y^{2}+16x–2y+13 = 0 |
B. x^{2}+4y^{2}-4x+8y+4 = 0 |
C. x^{2}+4y^{2}+4x–8y+4 = 0 |
D. 4x^{2}+y^{2}-16x–2y+13 = 0 |
E. 4x^{2}+y^{2}-16x+2y+13 = 0 |
Solution: The answer is E
The general form of the equation of an ellipse with, a vertical major axis, center (h,k), and major and minor axes of length 2a and 2b respectively, where a > b > 0 is given by,
From the graph above, notice that the major axis length, 2a = 4, and that the minor axis length, 2b = 2. Hence, a = 2 and b = 1. Since the center is (2,-1), then the equation of the given ellipse is,
Which simplifies to,